Choice D is correct. A line in the xy-plane with a slope of $m$ and a y-intercept of $left parenthesis 0 comma b right parenthesis$ can be defined by an equation in the form $y = m x + b$ . It’s given that line $r$ has a slope of $4$ and passes through the point $left parenthesis 0 comma 6 right parenthesis$ . It follows that $m equals 4$ and $b equals 6$ . Substituting $4$ for $m$ and $6$ for $b$ in the equation $y = m x + b$ yields $y = 4 x + 6$ . Therefore, the equation $y = 4 x + 6$ defines line $r$ .

Choice A is incorrect. This equation defines a line that has a slope of $negative 6$ , not $4$ , and passes through the point $left parenthesis 0 comma 4 right parenthesis$ , not $left parenthesis 0 comma 6 right parenthesis$ .

Choice B is incorrect. This equation defines a line that has a slope of $6$ , not $4$ , and passes through the point $left parenthesis 0 comma 4 right parenthesis$ , not $left parenthesis 0 comma 6 right parenthesis$ .

Choice C is incorrect. This equation defines a line that passes through the point $left parenthesis 0 comma negative 6 right parenthesis$ , not $left parenthesis 0 comma 6 right parenthesis$ .